论文标题
自适应多解决内部惩罚不连续的盖尔金方法，用于二阶形式的波动方程
An adaptive multiresolution interior penalty discontinuous Galerkin method for wave equations in second order form
论文作者
论文摘要
在本文中，我们提出了一类自适应多分辨率（也称为自适应稀疏网格）不连续的Galerkin（DG）方法，用于在空间中以二阶形式模拟标量波方程。这些方案的两种关键成分包括自适应功能空间中的内部惩罚DG公式和两类的多波管，以实现多解析。特别是，正式的Alpert的多波器用于根据分层结构来表达DG解决方案，并进一步引入插值多波武器，以在存在可变波速度或非线性源的存在下提高计算效率。提出了有关稳定性和所提出方法准确性的一些理论结果。提供了2D和3D中的基准数值测试，以验证该方法的性能。
In this paper, we propose a class of adaptive multiresolution (also called adaptive sparse grid) discontinuous Galerkin (DG) methods for simulating scalar wave equations in second order form in space. The two key ingredients of the schemes include an interior penalty DG formulation in the adaptive function space and two classes of multiwavelets for achieving multiresolution. In particular, the orthonormal Alpert's multiwavelets are used to express the DG solution in terms of a hierarchical structure, and the interpolatory multiwavelets are further introduced to enhance computational efficiency in the presence of variable wave speed or nonlinear source. Some theoretical results on stability and accuracy of the proposed method are presented. Benchmark numerical tests in 2D and 3D are provided to validate the performance of the method.
